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REVIEW 4 major objections 5 minor 95 references

Metabolic quantum limit to the information capacity of magnetoencephalography

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Metabolic energy, not sensor technology, sets a quantum upper bound on how much information magnetoencephalography can extract from the brain—about 2.6 million bits per second for a typical human head.

desk verdict The metabolic-ERL coupling is genuinely new and the spectral math is solid, but Eq. (15) is not a proven upper bound on MEG capacity—it is an estimate for one particular white-Gaussian source model. read the letter →

arxiv 2511.06401 v3 pith:D2GGXAHL submitted 2025-11-09 physics.bio-ph physics.comp-phquant-ph

E. Gkoudinakis , S. Li , I. K. Kominis This is my paper · ORCID
classification physics.bio-phphysics.comp-phquant-ph
keywords magnetoencephalographyinformationcapacityenergyresolutionlimitquantumsensingmetabolicpowerholographicboundlead-fieldoperatorShannon
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Magnetoencephalography (MEG) measures the brain's magnetic fields with quantum sensors, but no one had a technology-independent answer to how much information such measurements can fundamentally carry. This paper derives such an upper bound by combining the quantum energy-resolution limit of any magnetic sensor with the metabolic power the brain spends on the currents that create the fields. The result is a formula that depends only on geometry, metabolism, and Planck's constant, giving roughly 2.6 million bits per second for a typical human head. In the high-bandwidth regime the bound becomes an area-proportional, 'holographic' limit of about 6.6 Gbit/s. If correct, the bound also predicts a spatial Nyquist scale near 1 cm, beyond which extra sensors add no new information.

What carries the argument

The central object is the lead-field operator L, which maps current-dipole densities inside the head to the magnetic-field components outside, and its covariance operator K_Ω = LL*. Its eigenvalues κ_ℓ (computed for a spherical geometry as μ0²a² 2(ℓ+1)/((2ℓ+1)²(2ℓ+3)) (a/(a+d))^{2ℓ+1}) quantify how efficiently random currents excite independent spatial field modes. The information formula is a Shannon sum over these modes, with the energy-resolution limit setting the noise floor and the metabolic mapping V[J] = Pmb A_d λ/(2ρV) converting the brain's power budget into current variance. The trace of K_Ω controls the high-bandwidth holographic limit.

What would settle it

Use a whole-head MEG system with known sensor noise and a dense array resolving modes beyond ℓ≈20, measure the information rate of the recorded field, and compare it with Eq. (15) computed from the same geometry and metabolic parameters; an information rate exceeding the bound would falsify it.

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Extended reading notes

Core claim

The paper derives a technology-independent upper bound on the information rate of magnetoencephalography. It models the measurement as a linear map from currents in the head to magnetic fields outside, with covariance operator K_Ω = LL*. Combining Shannon's formula with the quantum energy-resolution limit (noise variance ≥ 2μ0ℏW) and a metabolic link (current variance = Pmb A_d λ/(2ρV)), it obtains I_W ≤ (W/2) Σ log2(1 + (Pmb A_d λ/(2ρV)) κ_ℓ/(2μ0ℏW)). For a spherical head model this evaluates to ≈2.6 Mbit/s at 1 kHz bandwidth; in the high-bandwidth limit the bound becomes a surface-area-proportional 'holographic' ceiling of ≈6.6 Gbit/s.

Load-bearing premise

The derivation assumes the brain's metabolic power is entirely converted into ohmic dissipation of the MEG-relevant axial dendritic currents, and that these currents can be treated as delta-correlated with an amplitude fixed by matching the integral of the actual exponential spatial correlation.

Editorial extensions

If this is right

  • Denser MEG arrays beyond the ~1 cm spatial Nyquist scale yield redundant measurements, not new information.
  • Temporal and spatial bandwidths compete: faster sampling raises quantum noise per mode, so one cannot independently increase both.
  • Current MEG systems (~0.4 Mbit/s) operate far below the ~2.6 Mbit/s ceiling, suggesting headroom for better information extraction.
  • The high-bandwidth holographic bound means a metabolically active source's magnetic information export is set by its surface area, not its volume or internal detail.
  • Information capacity should scale roughly linearly with metabolic power in the biological regime, testable through sleep-wake or task-driven metabolic changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct experimental check would be to measure the lead-field eigenvalue spectrum in a realistic head model and see whether information saturates at the predicted number of modes; deviations would show where the idealized spherical geometry fails.
  • The same metabolic-quantum argument could apply to other biomagnetic sources, such as cardiac fields, where a similar area-proportional information bound would be testable with existing magnetocardiography systems.
  • The framework hints at a practical discriminator between biological and artificial signal sources: artificial systems with broader bandwidth could approach the 6.6 Gbit/s holographic limit, while brains stay orders of magnitude below it.
  • If the metabolic mapping is right, altering the electrotonic length or dendritic cross-section (e.g., via pharmacological agents) should shift the bound, providing a controlled probe of the assumption.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper derives what it calls a 'metabolic quantum limit' to the information capacity of magnetoencephalography. The authors model the measurement as a linear lead-field operator L mapping neural current densities in a volume V to magnetic fields in an exterior region Ω, with noise obeying the energy resolution limit (ERL). They assume Gaussian delta-correlated current sources with covariance V[J]I_V and compute the mutual information in the eigenbasis of the compact operator KΩ=LL*, leading to Eq. (13). Using the metabolic relation V[J]=Pmb A_d λ/(2ρV) yields the main formula, Eq. (15), evaluated as ~2.6 Mbit/s for a spherical head with representative parameters. A high-bandwidth approximation gives Eq. (16), an area-law 'holographic' bound of ~6.6 Gbit/s. The paper also claims a finite angular bandwidth and an information-limited spatial scale of order 1 cm. The mathematical machinery of fixed-covariance Gaussian mutual information is internally consistent, and the spherical eigenvalue calculation is explicit, but the central claim that Eq. (15) is an upper bound on MEG information capacity is not established.

Significance. If Eq. (15) were a true capacity bound, it would provide a conceptually interesting link among metabolism, quantum sensing limits, and neuroimaging information content. The trace-class analysis, the spherical eigenvalue computation, and the explicit use of external ERL results are strengths; the calculation is checkable and the parameter choices are stated. However, as written the result is a mutual-information estimate for a particular delta-correlated Gaussian source model, not a maximized capacity. The paper also contains a numerical inconsistency between the abstract and body and an unsupported spatial-scale claim. The significance of the contribution therefore depends on whether the authors can either prove the required maximization or honestly reframe the result as a model-specific estimate.

major comments (4)
  1. [Eq. (15) and the surrounding 'main result'] Eq. (15) is stated as an upper bound I_W ≤ ..., but Eq. (13) is the mutual information for the specific Gaussian input with covariance V[J]I_V (Eq. 8). Shannon capacity is the maximum over input distributions; the metabolic constraint fixes only the scalar V[J] and does not constrain the shape of the source covariance. The lead-field eigenvalues decay as (a/R)^{2ℓ+1} (Eq. B16), so the channel is far from flat, and water-filling over the modes of L*L gives a larger mutual information for the same total dissipated power than the white/delta-correlated covariance. Thus Eqs. (15) and (16) are estimates for a delta-correlated source model, not demonstrated upper bounds. The word 'bound' in the central claim is therefore unjustified.
  2. [Metabolic mapping, 'For the last step of our derivation'] The key mapping V[J]=Pmb A_d λ/(2ρV) is a heuristic identification, not a derived constraint. It identifies total ohmic dissipation ∫ρJ²dV with the full metabolic power Pmb and replaces the exponential current correlation with a delta function by matching height and width. Real cortical currents are not delta-correlated at this amplitude, only a fraction of ohmic dissipation may generate MEG-relevant fields, and the single semi-infinite cable parameters (A_d, λ, ρ) are idealized. The numerical value 2.6 Mbit/s and the high-bandwidth bound Eq. (16) depend directly on this assumption. The paper should either justify this as an upper envelope or present it explicitly as a model-dependent estimate with a sensitivity analysis.
  3. [Abstract vs. body numerical/spatial claims] The abstract reports 2.2 Mbit/s, while the body reports 2.6 Mbit/s for the same W=1000 s⁻¹. Additionally, the abstract claims an information-limited spatial scale of order 1 cm, but no derivation of this scale appears in the body. The finite angular bandwidth is shown by the multipole expansion, but converting the mode cutoff into a spatial Nyquist scale requires a specific threshold definition (e.g., comparing eigenvalue contributions to the quantum noise floor at a chosen bandwidth). These are load-bearing stated results and must either be derived explicitly or removed from the abstract.
  4. [Experimental-sensitivity paragraph] The paragraph beginning 'The above can be probed experimentally' defines I'_W=dI_W/dPmb and writes I'_W=(1/ln2)Σ λℓ/(1+λℓPmb). In the stated biological regime λℓPmb≫1, each term tends to 1/Pmb, not to λℓPmb/Pmb, so the asymptotic result should be proportional to M/(Pmb ln2), not (Pmb/ln2)Σℓ. As written, the scaling with Pmb is inverted and dimensionally inconsistent. This affects the proposed experimental test and should be corrected.
minor comments (5)
  1. [Title] The title contains a typo: 'inform ation' should be 'information'.
  2. [Abstract] The 2.2 Mbit/s in the abstract should be reconciled with the 2.6 Mbit/s in the body.
  3. [Figure 1 caption] The caption contains an apparent rendering artifact: a long string of '/gid...' tokens. This should be fixed before submission.
  4. [Sensitivity paragraph] The symbol Σℓ is used both as a sum and as the total number of participating modes; this should be clarified with distinct notation.
  5. [Units in Eq. (6)] The stated units of V[J] (A²/m) should be checked against the definitions of J and the lead-field integral in Eq. (1); the manuscript should define the units of J explicitly.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Eq. (15) is a forward substitution of external biophysical inputs and the ERL; the only self-citation is non-load-bearing.

full rationale

The derivation chain is explicit and non-circular: the lead-field operator L is defined from the Biot-Savart law (Eqs. 1-5); the current and noise covariances are declared modeling assumptions (Eqs. 6-9); the ERL fixes V[b] >= 2*mu0*hbar*W (Eq. 14); the cable equation fixes V[J] = Pmb*A_d*lambda/(2*rho*V) by matching ohmic dissipation to metabolic power; and Eq. (15) is obtained by substituting these external inputs into the Gaussian mutual-information formula. No term of the final bound is assumed as an input. The only author self-citation is [63] for the energy resolution limit, but that limit is independently established by the external RMP Colloquium [62], so it is not load-bearing. The skeptic's point that no maximization over source statistics is performed is a correctness/validity concern about the word 'bound', not a circularity: the white Gaussian model is stated as an assumption (Eq. 8), and the resulting I_W is conditional on that model. Overall, the paper contains no definitional circularity, fitted parameter masquerading as prediction, or uniqueness conclusion imported from the authors' prior work.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the externally established ERL, standard Shannon theory, a Gaussian delta-correlated source model, and a cable-theory mapping of metabolic power to current variance. No invented entities appear. The modeling assumptions are stated but not stress-tested; the numerical value depends on literature-valued parameters.

free parameters (5)
  • W (sampling rate) = 1000 s^{-1}
    Chosen for the numerical example; the capacity should be evaluated at W=2BJ where BJ is the source bandwidth, which is not specified.
  • a (head radius) = 8 cm
    Representative human head radius used in the spherical model; enters the eigenvalues κℓ and the numerical bound.
  • d (sensor-to-head distance) = 1.3 cm
    Minimum distance between source volume and observation region; sets the decay rate of eigenvalues (a/(a+d))^{2ℓ+1}.
  • Pmb (metabolic power) = 12 mW
    Estimated from the biophysical budget (0.115 fJ per EPSP × 1.1e14 events/s); directly scales V[J] and the bound.
  • Cable parameters (A_d, λ, ρ) = A_d=π(0.5µm)^2, λ=0.3mm, ρ=1Ωm
    Literature values for dendritic cross-section, electrotonic length, and intracellular resistivity; set the ratio V[J]/Pmb.
assumptions (7)
  • domain assumption Energy resolution limit: ε = (δB)²v/(2μ0) ≥ ℏ per unit bandwidth
    Adopted from Mitchell & Alvarez [62] and Kominis [63]; the paper's bound on noise variance V[b] ≥ 2μ0ℏW rests on this.
  • domain assumption Current sources are Gaussian, zero-mean, delta-correlated with isotropic variance V[J] (Eqs. 6, 8)
    This stochastic model of neural currents is stated as the source model; it determines the mode SNR and the Shannon sum.
  • domain assumption Sensor noise is additive, white, delta-correlated with covariance V[b]IΩ (Eq. 7)
    Models a continuum of independent point sensors; the ERL fixes V[b].
  • domain assumption Homogeneous conductivity in the source region (Eq. 1-2)
    The lead-field operator uses the free-space Biot-Savart kernel; real head tissue is inhomogeneous, which would alter the eigenvalues.
  • standard math Shannon formula for parallel Gaussian channels (Eq. 13)
    Mutual information of independent Gaussian channels in the eigenbasis of KΩ.
  • domain assumption Cable model: axial current decays exponentially, I(x)=I0 e^{-x/λ}
    Semi-infinite cylindrical cable model for EPSP currents (Johnston & Wu); used to derive V_c and the ohmic dissipation.
  • standard math Monopole (ℓ=0) magnetic field mode is unphysical and excluded from the spectral sum
    Divergence-free currents cannot produce a monopole exterior field; exclusion is a standard harmonic analysis step.

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Pith. "Pith review of Metabolic quantum limit to the information capacity of magnetoencephalography." pith.science (2026). https://pith.science/paper/D2GGXAHL

@misc{pith2026251106401,
  author       = {Pith},
  title        = {Pith review of: Metabolic quantum limit to the information capacity of magnetoencephalography},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D2GGXAHL}},
  note         = {Machine review of arXiv:2511.06401}
}
abstract

Magnetoencephalography measures the magnetic fields generated by neural currents using quantum sensors such as superconducting quantum interference devices and atomic magnetometers. Here we combine the energy resolution limit of magnetic sensing with the metabolic power available to neural currents to derive a technology-independent bound on the information capacity of MEG. The bound factorizes into geometry, metabolism, and Planck's constant, and gives an estimated maximum information rate of 2.2~Mbit/s for representative human-brain parameters. Further, we show that the externally measurable magnetic field has a finite angular bandwidth, with high multipole components being geometrically attenuated and falling below the quantum-limited noise floor. This yields an information-limited spatial scale of order $1~{\rm cm}$ and renders the accessible measurement space effectively finite-dimensional. The energy resolution limit therefore defines an information-theoretic Nyquist scale for magnetoencephalography, beyond which denser spatial sampling provides redundant measurements rather than additional recoverable information. Since the energy resolution limit also makes the noise variance grow linearly with measurement bandwidth, temporal and spatial bandwidths compete, producing a fundamental spatio-temporal trade-off. These results show how quantum-limited measurements constrain the observable complexity and information content of noninvasive brain imaging, providing a quantitative link between fundamental physics and neuroscience.

Figures

Figures reproduced from arXiv: 2511.06401 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The first 30 eigenvalues of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

Works this paper leans on

95 extracted references

  1. [1]

    Cohen, Magnetoencephalography: Detection of the brain’s electrical activity with a superconduct- ing magnetometer, Science 175, 664 (1972)

    D. Cohen, Magnetoencephalography: Detection of the brain’s electrical activity with a superconduct- ing magnetometer, Science 175, 664 (1972)

    1972

  2. [2]

    S. Sato, M. Balish, and R. Muratore, Principles of magnetoencephalography, J. Clin. Neurophysiol. 8, 144 (1991)

    1991

  3. [3]

    Hämäläinen, R

    M. Hämäläinen, R. Hari, R. J. Ilmoniemi, J. Knuu- tila, and O. V. Lounasmaa, Magnetoencephalogra- phy - theory, instrumentation, and applications to noninvasive studies of the working human brain , Rev. Mod. Phys. 65, 413 (1993)

    1993

  4. [4]

    For an analytically tractable example from which we can readily obtain a numerical estimate, we con- sider a spherical geometry, i.e

    for W = 2BJ . For an analytically tractable example from which we can readily obtain a numerical estimate, we con- sider a spherical geometry, i.e. a source region of radius a and observation region consisting of points r such that |r| ≥ a + d. We use a head ra- dius a = 8 cm and d = 1 .3 cm. The eigenval- ues of KΩ, derived in the End Matter, are κℓ = µ2...

  5. [5]

    There- fore, E[ ˜β2 ℓ ] = V[J] κℓ + V[b]

    and (8) we get E [ ⟨L [J], uℓ⟩ 2] = V[J] ⟨ uℓ, LL∗uℓ⟩ = V[J] κℓ, and from ( 9), E [ ⟨ b, uℓ⟩ 2] = V[b]⟨ uℓ, uℓ⟩ = V[b]. There- fore, E[ ˜β2 ℓ ] = V[J] κℓ + V[b]. (12) The eigenfunctions uℓ(r) describe spatial magnetic- field patterns that fluctuate independently. Thus, by Shannon’s formula, the total information obtained from a spatially continuous measurem...

  6. [6]

    In the biological regime under considera- tion, it is λℓPmb ≫ 1, thus I ′ W = ( Pmb/ ln 2) ∑ ℓ, where ∑ ℓ is the total number of modes participat- ing

    as 1 + Pmbλℓ, we define the sensitivity of information to metabolic drive as I ′ W = dIW /dPmb = (1 / ln 2) ∑ ℓ λℓ/(1 + λℓPmb). In the biological regime under considera- tion, it is λℓPmb ≫ 1, thus I ′ W = ( Pmb/ ln 2) ∑ ℓ, where ∑ ℓ is the total number of modes participat- ing. Thus a scaling of I ′ W with Pmb can in principle reveal both the metabolic law (

  7. [7]

    The information bound intertwining geometric, metabolic, and quantum components can be gen- eralized towards several directions

    and the number of modes contributing, although within the demand- ing constraint that the metabolic power can practi- cally vary in the range of only 5% [ 75, 83]. The information bound intertwining geometric, metabolic, and quantum components can be gen- eralized towards several directions. First, one may derive testable scaling laws linking network geom...

  8. [8]

    C. D. Gratta, V. Pizzella, F. Tecchio and G. L. Romani, Magnetoencephalography - a noninvasive brain imaging method with 1 ms time resolution , Rep. Prog. Phys. 64, 1759 (2001)

    2001

Show all 95 references
  1. [9]

    Nolte, The magnetic lead field theorem in the quasi-static approximation and its use for mag- netoencephalography forward calculation in realis- tic volume conductors , Phys

    G. Nolte, The magnetic lead field theorem in the quasi-static approximation and its use for mag- netoencephalography forward calculation in realis- tic volume conductors , Phys. Med. Biol. 48, 3637 (2003)

    2003

  2. [10]

    J. W. Wheless, E. Castillo, V. Maggio, H. L. Kim, J. I. Breier, P. G. Simos, and A. C. Papanicolaou, Mag- netoencephalography (MEG) and magnetic source imaging (MSI) , Neurologist 10, 138 (2004)

    2004

  3. [11]

    sig- nal

    as “sig- nal” and “noise”, and using independence and zero mean, we have E[ ˜βℓ] = 0 and E[ ˜β2 ℓ ] = E [ ⟨L [J], uℓ⟩ 2] +E [ ⟨ b, uℓ⟩ 2] . Using (

  4. [12]

    R. C. Knowlton, K. D. Laxer, M. J. Aminoff, T. P. L. Roberts, S. T. C. Wong, and H. A. Rowley, Magnetoencephalography in partial epilepsy: Clini- cal yield and localization accuracy , Annals Neurol. 42, 622 (1997)

    1997

  5. [13]

    O. V. Lounasmaa, M. Hämäläinen, R. Hari, and R. Salmelin, Information processing in the human brain: magnetoencephalographic approach , Proc. Natl. Acad. Sci. USA 93, 8809 (1996)

    1996

  6. [14]

    yields IW ≤ W 2 ∑ ℓ log2 ( 1 + PmbAdλ 2ρV κℓ 2µ0ℏW ) (15) This expression is the main result of this work. As stated in the introduction, it is casted in three fac- tors: a geometric factor, κℓ, reflecting the geomet- ric coupling of current dipoles into magnetic fields, a metab...

  7. [15]

    It is seen that the more sensitive the sensor, the more spatial modes of KΩ are required to saturate IW

    by letting the sum over ℓ extend from 1 to m = 1 , 2, ..., 30, and generalizing the ERL to be in the range from ℏ (the fundamental limit) up to 10 4ℏ. It is seen that the more sensitive the sensor, the more spatial modes of KΩ are required to saturate IW . The above can be pro...

  8. [16]

    Hari and N

    R. Hari and N. Forss, Magnetoencephalography in the study of human somatosensory cortical process- ing, Phil. Trans. R. Soc. B 354, 1145 (1999)

    1999

  9. [17]

    Vrba and S

    J. Vrba and S. E. Robinson, Signal processing in magnetoencephalography, Methods 25, 249 (2001)

    2001

  10. [18]

    A. S. Fokas, Y. Kurylev, and V. Marinakis, The unique determination of neuronal currents in the brain via magnetoencephalography , Inverse Prob. 20, 1067 (2004)

    2004

  11. [19]

    Hillebrand, K

    A. Hillebrand, K. D. Singh, I. E. Holliday, P. L. Furlong, and G. R. Barnes, A new approach to neuroimaging with magnetoencephalography , Hum. Brain Mapp. 25, 199 (2005)

    2005

  12. [20]

    D. M. Goldenholz, S. P. Ahlfors, M. S. Hämäläi- nen, D. Sharon, M. Ishitobi, L. M. Vaina, and S. M. Stufflebeam, Mapping the signal-to-noise-ratios of cortical sources in magnetoencephalography and electroencephalography, Hum. Brain Mapp. 30, 1077 (2009)

    2009

  13. [21]

    C. J. Stam, Use of magnetoencephalography (MEG) to study functional brain networks in neurodegener- ative disorders, J. Neurol. Sci. 289, 128 (2010)

    2010

  14. [22]

    Hari and R

    R. Hari and R. Salmelin, Magnetoencephalography: from SQUIDs to neuroscience, Neuroimage 61, 386 (2012)

    2012

  15. [23]

    Baillet, Magnetoencephalography for brain elec- trophysiology and imaging, Nature Neurosci

    S. Baillet, Magnetoencephalography for brain elec- trophysiology and imaging, Nature Neurosci. 20, 327 (2017)

    2017

  16. [24]

    Koelle, R

    D. Koelle, R. Kleiner, F. Ludwig, E. Dantsker, and J. Clarke, High-transition-temperature super- conducting quantum interference devices, Rev. Mod. Phys. 71, 631 (1999)

    1999

  17. [25]

    Vrba and S

    J. Vrba and S. E. Robinson, SQUID sensor array configurations for magnetoencephalography applica- tions, Supercond. Sci. and Technol. 15, R51 (2002)

    2002

  18. [26]

    R. L. Fagaly, Superconducting quantum interference device instruments and applications , Rev. Sci. In- strum. 77, 101101 (2006)

    2006

  19. [27]

    Yang, H.-E

    H.-C. Yang, H.-E. Horng, S. Y. Yang and S.-H. Liao, Advances in biomagnetic research using high-Tc su- perconducting quantum interference devices , Super- cond. Sci. and Technol. 22, 093001 (2009)

    2009

  20. [28]

    Öisjöen, J

    F. Öisjöen, J. F. Schneiderman, G. A. Figueras, M. L. Chukharkin, A. Kalabukhov, A. Hedström, M. Elam, and D. Winkler, High-Tc superconduct- ing quantum interference device recordings of spon- taneous brain activity: Towards high- Tc magne- toencephalography, Appl. Phys. Lett....

    2012

  21. [29]

    M. I. Faley, U. Poppe, R. E. Dunin-Borkowski, M. Schiek, F. Boers, H. Chocholacs, J. Dammers, E. Eich, N. J. Shah, A. B. Ermakov, V. Y. Slobod- chikov, Y. V. Maslennikov, and V. P. Koshelets, High-Tc DC SQUIDs for magnetoencephalography, IEEE Trans. Appl. Supercond. 23, 1600705 (2013)

    2013

  22. [30]

    I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, A subfemtotesla multichannel atomic magnetometer, Nature 422, 596 (2003)

    2003

  23. [31]

    Budker and M

    D. Budker and M. V. Romalis, Optical magnetome- try, Nature Phys. 3, 227 (2007)

    2007

  24. [32]

    Sheng, S

    D. Sheng, S. Li, N. Dural, and M. V. Romalis, Sub- femtotesla scalar atomic magnetometry using multi- pass cells , Phys. Rev. Lett. 110, 160802 (2013)

    2013

  25. [33]

    H. Xia, A. B.-A. Baranga, D. Hoffman, and M. V. Romalis, Magnetoencephalography with an atomic magnetometer, Appl. Phys. Lett. 89, 211104 (2006)

    2006

  26. [34]

    C. N. Johnson, P. D. D. Schwindt, and M. Weisend, 8 Multi-sensor magnetoencephalography with atomic magnetometers, Phys. Med. Biol. 58, 6065 (2013)

    2013

  27. [35]

    K. Kim, S. Begus, H. Xia, S.-K. Lee, V. Jazbin- sek, Z. Trontelj, and M. V. Romalis, Multi-channel atomic magnetometer for magnetoencephalography: A configuration study , Neuroimage 89, 143 (2014)

    2014

  28. [36]

    O. Alem, A. M. Benison, D. S. Barth, J. Kitch- ing, and S. Knappe, Magnetoencephalography of epilepsy with a microfabricated atomic magnetome- ter, J. Neurosci. 34, 14324 (2014)

    2014

  29. [37]

    A. P. Colombo, T. R. Carter, A. Borna, Y.-Y. Jau, C. N. Johnson, A. L. Dagel, and P. D. D. Schwindt, Four-channel optically pumped atomic magnetome- ter for magnetoencephalography , Opt. Express 24, 15403 (2016)

    2016

  30. [38]

    E. Boto, S. Meyer, V. Shah, O. Alem, S. Knappe, P. Kruger, M. Fromhold, P. Morris, R. Bowtell, G. Barnes, M. Brookes, and M. Lim, A new genera- tion of magnetoencephalography: Room temperature measurements using optically-pumped magnetome- ters, Neuroimage 149, 404 (2017)

    2017

  31. [39]

    Sheng, S

    J. Sheng, S. Wan, Y. Sun, R. Dou, Y. Guo, K. Wei, K. He, J. Qin, and J.-H. Gao, Magnetoencephalogra- phy with a Cs-based high-sensitivity compact atomic magnetometer, Rev. Sci. Instr. 88, 094304 (2017)

    2017

  32. [40]

    Borna, T

    A. Borna, T. R. Carter, J. D. Goldberg, A. P. Colombo, Y.-Y. Jau, C. Berry, J. McKay, J. Stephen, M. Weisend, and P. D. D. Schwindt, A 20- channel magnetoencephalography system based on optically pumped magnetometers , Phys. Biol. Med. 62, 8909 (2017)

    2017

  33. [41]

    E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. S. Meyer, L. D. Muñoz, K. J. Mullinger, T. M. Tierney, S. Bestmann, G. R. Barnes, R. Bowtell, and M. J. Brookes, Moving magnetoencephalogra- phy towards real-world applications with a wearable system, Nature 555, 657 (2018)

    2018

  34. [42]

    W. Xiao, C. Sun, L. Shen, Y. Feng, M. Liu, Y. Wu, X. Liu, T. Wu, X. Peng, and H. Guo, A movable unshielded magnetocardiography system, Science Ad- vances 9, eadg1746 (2018)

    2018

  35. [43]

    T. M. Tierney, N. Holmes, S. Mellor, J. D. López, G. Roberts, R. M. Hill, E. Boto, J. Leggett, V. Shah. M. J. Brookes, R. Bowtell, and G. R. Barnes, Optically pumped magnetometers: From quantum origins to multi-channel magnetoencephalography , Neuroimage 199, 598 (2019)

    2019

  36. [44]

    Iivanainen, R

    J. Iivanainen, R. Zetter, M. Grön, K. Hakkarainen, and L. Parkkonen, On-scalp MEG system utilizing an actively shielded array of optically-pumped mag- netometers, Neuroimage 194, 244 (2019)

    2019

  37. [45]

    D. N. Barry, T. M. Tierney, N. Holmes, E. Boto, G. Roberts, J. Leggett, R. Bowtell, M. J. Brookes, G. R. Barnes, E. A. Maguire, Imaging the hu- man hippocampus with optically-pumped magnetoen- cephalography, Neuroimage 203, 116192 (2019)

    2019

  38. [46]

    K. He, S. Wan, J. Sheng, D. Liu, C. Wang, D. Li, L. Qin, S. Luo, J. Qin, and J.-H. Gao, A high- performance compact magnetic shield for optically pumped magnetometer-based magnetoencephalogra- phy, Rev. Sci. Instr. 90, 064102 (2019)

    2019

  39. [47]

    Zhang, S

    G. Zhang, S. Huang, F. Xu, Z. Hu, and Q. Lin, Multi-channel spin exchange relaxation free magne- tometer towards two-dimensional vector magnetoen- cephalography, Opt. Express 27, 597 (2019)

    2019

  40. [48]

    Labyt, M.-C

    E. Labyt, M.-C. Corsi, W. Fourcault, A. P. Laloy, F. Bertrand, and F. Lenouvel, Magnetoencephalog- raphy with optically pumped 4He magnetometers at ambient temperature , IEEE Trans. Med. Imaging 38, 90 (2019)

    2019

  41. [49]

    Zhang, W

    R. Zhang, W. Xiao, Y. Ding, Y. Feng, X. Peng, L. Shen, C. Sun, T. Wu, Y. Wu, Y. Yang, Z. Zheng, X. Zhang, J. Chen, and H. Guo, Recording brain activities in unshielded Earth’s field with op- tically pumped atomic magnetometers , Sci. Adv. 6, eaba8792 (2020)

    2020

  42. [50]

    Borna , T

    A. Borna , T. R. Carter, A. P. Colombo, Y.-Y. Jau, J. McKay, M. Weisend, S. Taulu, J. M. Stephen, and P. D. D. Schwindt, Non-Invasive functional-brain- imaging with an OPM-based magnetoencephalogra- phy system , PLOS One 15, 1 (2020)

    2020

  43. [51]

    Vivekananda, S

    U. Vivekananda, S. Mellor, T. M. Tierney, N. Holmes, E. Boto, J. Leggett, G. Roberts, R. M. Hill, V. Litvak, M. J. Brookes, R. Bowtell, G. R. Barnes, and M. C. Walker, Optically pumped magne- toencephalography in epilepsy , Annals Clin. Trans- lat. Neurol. 7, 397 (2020)

    2020

  44. [52]

    M. Rea, E. Boto, N. Holmes, R. Hill, J. Osborne, N. Rhodes, J. Leggett, L. Rier, R. Bowtell, V. Shah, and M. J. Brookes, A 90-channel triaxial mag- netoencephalography system using optically pumped magnetometers, Ann. NY Acad. Sci. 1517, 107 (2022)

    2022

  45. [53]

    Feys , P

    O. Feys , P. Corvilain, A. Aeby, C. Sculier, N. Holmes, M. Brookes, S. Goldman, V. Wens, and X. De Tiège, On-scalp optically pumped magnetometers versus cryogenic magnetoencephalography for diag- nostic evaluation of epilepsy in school-aged children , Radiology 304, 429 (2022)

    2022

  46. [54]

    B. Bao, Y. Hua, R. Wang, and D. Li, Quantum- based magnetic field sensors for biosensing , Adv. Quantum Technol. 6, 2200146 (2023)

    2023

  47. [55]

    R. T. Wakai, A. C. Leuthold, and C. B. Martin, Fetal auditory evoked responses detected by magne- toencephalography, Am. J. Obster. Gynec. 174, 1484 (1996)

    1996

  48. [56]

    F. J. P. Langheim, A. C. Leuthold, and A. P. Georgopoulos, Synchronous dynamic brain networks revealed by magnetoencephalography , Proc. Natl. Acad. Sci. USA 103, 455 (2006)

    2006

  49. [57]

    A. A. Ioannides, Magnetoencephalography as a re- search tool in neuroscience: State of the art , Neuro- scientist 12, 524 (2006)

    2006

  50. [58]

    Parkkonen, N

    L. Parkkonen, N. Fujiki, and J. P. Mäkelä, Sources of auditory brainstem responses revisited: Contribu- tion by magnetoencephalography, Hum. Brain Mapp. 30, 1772 (2009)

    2009

  51. [59]

    R. M. Cichy, A. Khosla, D. Pantazis, and A. Oliva, Dynamics of scene representations in the human brain revealed by magnetoencephalography and deep neural networks, Neuroimage 153, 346 (2017)

    2017

  52. [60]

    Gross, Magnetoencephalography in cognitive neu- 9 roscience: A primer, Neuron 104, 189 (2019)

    J. Gross, Magnetoencephalography in cognitive neu- 9 roscience: A primer, Neuron 104, 189 (2019)

    2019

  53. [61]

    R. M. Cichy, F. M. Ramirez, and D. Pantazis, Can visual information encoded in cortical columns be decoded from magnetoencephalography data in hu- mans?, Neuroimage 121, 193 (2015)

    2015

  54. [62]

    D. F. Rose, P. D. Smith, and S. Sato, Magnetoen- cephalography and epilepsy research , Science 238, 329 (1987)

    1987

  55. [63]

    R. C. Knowlton and J. Shih, Magnetoencephalogra- phy in epilepsy , Epilepsia 45, 61 (2004)

    2004

  56. [64]

    Magnetoencephalography in neurosurgery , Neuro- surgery 59, 493 (2006)

    2006

  57. [65]

    S. M. Stufflebeam, N. Tanaka, and S. P. Ahlfors, Clinical applications of magnetoencephalography , Hum. Brain Mapp. 30, 1813 (2009)

    2009

  58. [66]

    I. S. Mohamed, S. A. Gibbs, M. Robert, A. Bouthillier, J.-M. Leroux, and D. K. Nguyen, The utility of magnetoencephalography in the presurgical evaluation of refractory insular epilepsy , Epilepsia 54, 1950 (2013)

    1950

  59. [67]

    T. W. Wilson, E. Heinrichs-Graham, A. L. Proskovec, and T. J. McDermott, Neuroimaging with magnetoencephalography: A dynamic view of brain pathophysiology, Transl. Res. 175, 17 (2016)

    2016

  60. [68]

    P. K. Kemppainen and R. J. Ilmoniemi, Channel ca- pacity of multichannel magnetometers , in Advances in biomagnetism , edited by (S. J. Williamson et al., Plenum Press, New York, 1989)

    1989

  61. [69]

    M. W. Mitchell and S. P. Alvarez, Colloquium: Quantum limits to the energy resolution of magnetic field sensors , Rev. Mod. Phys. 92, 021001 (2020)

    2020

  62. [70]

    I. K. Kominis, Quantum thermodynamic deriva- tion of the energy resolution limit in magnetometry , Phys. Rev. Lett. 133, 263201 (2024)

    2024

  63. [71]

    J. F. Schneiderman, Information content with low- vs. high-Tc SQUID arrays in MEG recordings: The case for high-Tc SQUID-based MEG , J. Neurosci. Meth. 222, 42 (2014)

    2014

  64. [72]

    Iivanainen, M

    J. Iivanainen, M. Stenroos, and L. Parkkonen, Mea- suring MEG closer to the brain: Performance of on- scalp sensor arrays , Neuroimage, 147, 542 (2017)

    2017

  65. [73]

    Skidchenko, N

    E. Skidchenko, N. Yavich, A. Butorina, M. Os- tras, P. Vetoshko, M. Malovichko, and N. Koshev, Yttrium-Iron Garnet magnetometer in MEG: Ad- vance towards multi-channel arrays , Sensors 23, 4256 (2023)

    2023

  66. [74]

    D. B. Geselowitz, On bioelectric potentials in an in- homogeneous conductor, Biophysical J. 7, 1 (1967)

    1967

  67. [75]

    D. B. Geselowitz, On the Magnetic Field Gener- ated Outside an Inhomogeneous Volume Conductor by Internal Current Sources , IEEE Trans. Magn. 6, 346 (1970)

    1970

  68. [76]

    Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem , Phys

    J. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem , Phys. Med. Biol. 32, 11 (1987)

    1987

  69. [77]

    J. C. Mosher, R. M. Leahy, and P. S. Lewis, EEG and MEG: Forward Solutions for Inverse Methods , IEEE Trans. Biomed. Eng. 46, 245 (1999)

    1999

  70. [78]

    Plonsey, The nature of sources of bioelectric and biomagnetic fields , Biophysical J

    R. Plonsey, The nature of sources of bioelectric and biomagnetic fields , Biophysical J. 39, 309 (1982)

    1982

  71. [79]

    Johnston and S

    D. Johnston and S. M.-S. Wu, Foundations of cellu- lar neurophysiology (MIT Press, Cambridge 1995)

    1995

  72. [80]

    Attwell and S

    D. Attwell and S. B. Laughlin, An Energy budget for signaling in the grey matter of the brain , J. Cereb. Blood Flow Metab. 21, 1133 (2001)

    2001

  73. [81]

    Lennie, The cost of cortical computation , Current Biol

    P. Lennie, The cost of cortical computation , Current Biol. 13, 493 (2003)

    2003

  74. [82]

    M. E. Raichle, Two views of brain function , Trends Cogn. Sci. 14, 180 (2010)

    2010

  75. [83]

    Howarth, C

    C. Howarth, C. M. Peppiatt-Wildman, and D. At- twell, The energy use associated with neural com- putation in the cerebellum , J. Cereb. Blood Flow Metab. 30, 403 (2010)

    2010

  76. [84]

    Howarth, P

    C. Howarth, P. Gleeson, and D. Attwell, Updated energy budgets for neural computation in the neo- cortex and cerebellum , J. Cereb. Blood Flow Metab. 32, 1222 (2012)

    2012

  77. [85]

    J. J. Harris and D. Attwell, The energy of CNS white matter, J. Neurosci. 32, 356 (2012)

    2012

  78. [86]

    R. J. Clarke, M. Catauro, H. H. Rasmussen, and H. Apell, Quantitative calculation of the role of the Na+,K+-ATPase in thermogenesis , Biochim. Bio- phys. Acta 1827, 1205 (2013)

    2013

  79. [87]

    Engl and D

    E. Engl and D. Attwell, Non-signaling energy use in the brain , J. Physiol. 16, 3417 (2015)

    2015

  80. [88]

    E. Engl, R. Jolivet, C. N. Hall, and D. Attwell, Non- signalling energy use in the developing rat brain , J. Cereb. Blood Flow Metab. 37, 951 (2017)

    2017

  81. [89]

    Y. Yu, P. Herman, D. L. Rothman, D. Agarwal, and F. Hyder, Evaluating the gray and white matter energy budgets of human brain function , J. Cereb. Blood Flow Metab. 38, 1339 (2017)

    2017

  82. [90]

    S. D. Jamadar, A. Behler, H. Deery, and M. Breaks- pear, The metabolic costs of cognition ,’Trends Cogn. Sci. 29, 541 (2025)

    2025

  83. [91]

    van Uitert, D

    R. van Uitert, D. Weinstein, and C. Johnson, Vol- ume Currents in Forward and Inverse Magnetoen- cephalographic Simulations Using Realistic Head Models, Annals Biomed. Eng. 31, 21 (2003)

    2003

  84. [92]

    Deffner and S

    S. Deffner and S. Campbell, Quantum thermody- namics (Morgan & Claypool Publishers, 2019)

    2019

  85. [93]

    M. Zhu, T. He, and C. Lee, Technologies toward next generation human machine interfaces: From machine learning enhanced tactile sensing to neu- romorphic sensory systems , Appl. Phys. Rev. 7, 031305 (2020)

    2020

  86. [94]

    R. M. Wald, The thermodynamics of black holes , Living Rev. in Rel. 4, 6 (2001)

    2001

  87. [95]

    X. Guo, P. Wang, and H. Yang, Membrane paradigm and holographic DC conductivity for nonlinear elec- trodynamics, Phys. Rev. D 98, 026021 (2018)

    2018

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